Quantum discontinuity fixed point and renormalization group flow of the Sachdev-Ye-Kitaev model

Abstract

We determine the global renormalization group (RG) flow of the Sachdev-Ye-Kitaev (SYK) model. This flow allows for an understanding of the surprising role of critical slowing down at a quantum first-order transition in strongly-correlated electronic systems. From a simple truncation of the infinite hierarchy of the exact functional RG flow equations we identify several fixed points: Apart from a stable fixed point, associated with the celebrated non-Fermi liquid state of the model, we find another stable fixed point related to an integer-valence state. These stable fixed points are separated by a discontinuity fixed point with one relevant direction, describing a quantum firstorder transition. Most notably, the fermionic spectrum continues to be quantum critical even at the discontinuity fixed point. This rules out a description of this quantum first-order transition in terms of a local effective Ising variable that is established for classical transitions. It reveals that quantum phase coexistence can be a genuine critical state of matter.

Breakdown and absence of quasiparticles in Kitaev’s models

“…1.2.1, we find an unexpected result: strongly correlated critical fluctuations at a discontinuous quantum phase transition. The structure of this chapter closely follows our publication [3]. In Sec.…”

“…In our case, we have a quantum phase transition at zero temperature and have no spatial degrees of freedom, and Fisher and Berker's interpretation does not apply straightforwardly. In our paper [3], we discuss the possibility that a quantum superposition of the nFL and IV phases is realized at the transition. The analogue of the diverging length scale would then be a diverging tunneling time scale.…”

“…The second part is based on our publication [3]. There, we perform a scaling analysis in a simple fermionic toy model, the Sachdev-Ye-Kitaev (SYK) model [12].…”

“…For a representative point in the special parameter region, we use these results to numerically calculate the magnon damping, which is to leading order caused by the decay of single magnons into two. We also calculate the dynamical structure factor of the magnons.The second part of this thesis is based on our publication [3], where we use the functional renormalization group to analyze a discontinuous quantum phase transition towards a non-Fermi liquid phase in the Sachdev-Ye-Kitaev (SYK) model. In this thesis, we perform a disorder average over the random interactions in the SYK model.…”

“…The second part of this thesis is based on our publication [3], where we use the functional renormalization group to analyze a discontinuous quantum phase transition towards a non-Fermi liquid phase in the Sachdev-Ye-Kitaev (SYK) model. In this thesis, we perform a disorder average over the random interactions in the SYK model.…”